Bi-banded Paths, a Bijection and the Narayana Numbers

Details Bi-banded Paths, a Bijection and the Narayana Numbers Bi-banded Paths, a Bijection and the Narayana Numbers

2010-05-10

arxiv.org/abs/1005.1521v1

Mathematics

Combinatorics

10 pages, 5 figures

Scientific paper

We find a bijection between bi-banded paths and peak-counting paths, applying to two classes of lattice paths including Dyck paths. Thus we find a new interpretation of Narayana numbers as coefficients of weight polynomials enumerating bi-banded Dyck paths, which class of paths has arisen naturally in previous literature in a solution of the stationary state of the `TASEP' stochastic process.

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